SOLUTION: How to solve whether or not the functions are inverses of each other? 1)F(x)=6x-7, g(x)=(x-6)/7 and 2) f(x)=3/(x+7), g(x)=(7x+3)/x

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Question 681109: How to solve whether or not the functions are inverses of each other?
1)F(x)=6x-7, g(x)=(x-6)/7
and
2) f(x)=3/(x+7), g(x)=(7x+3)/x

Answer by funmath(2933)   (Show Source): You can put this solution on YOUR website!
Tell whether or not the functions are inverses of each other?
1)F(x)=6x-7, g(x)=(x-6)/7
and
2) f(x)=3/(x+7), g(x)=(7x+3)/x

If they are inverses, then their composite functions have to equal x

That is f(g(x))=x and g(f(x))=x.
1.
You will substitute g(x) in for the x's in f(x).


Get a common denominator...


since it did not simplify to x, they are not inverses of each other.

2. f(g(x))=f((7x+3)/x)


Multiply the top and the bottom by x to clear the complex fraction.



This also doesn't simplify to x and therefore are not inverses.
******************************************************************
Just to clarify....this is an example where they ARE inverses.
3. and


to clear the complex fraction, multiply the top and bottom by x




f(x) and g(x) ARE inverses in this case because f(g(x))=x.
*Note...g(f(x))=x as well....give it a try.
Hope that helped. Happy Calculating!!!!

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